First, let me address the fact that you can see the grain of the wood. Oak is what is called an "Open grain" wood. Unless your willing to apply a wood filler in a similar fasion to the way you would finish drywall, you will always see the grain. If you were looking for a smooth finish, you would have been better off using Birch or Maple.
OK, That aside, it sounds like all you need to do is give the cabinets a good sanding and then repaint them.
Personally, I prefer to use oil paints on cabinetry. It's tougher and will stand up to the handling that cabinets are subjected to. If your painter used oil paints, then just sand with medium grit paper and then clean up the dust with a tack cloth and apply 1 or 2 coats of oil paint. If latex was used then you either need to stick to latex or use suitable primer to bond the alkyd to the latex.
In both cases, it is important to take the time to clean all the dust off with a tack cloth. I also remove the doors, hinges, knobs and other hardware. Much easier to keep the paint off of the hardware that way.